Novel method to establish equation of ZN helicoid and meshing limit line of related worm drive

Abstract

According to the definition, the straight sided normal profile helicoid is established. It is strictly proved that the normal section of straight sided normal profile helicoid is straight line and the cross-section is extended involute, and the section curve of axial section is obtained. The calculation formula of the guide cylinder radius under different installation modes of ZN-type worm is obtained. The meshing limit line equation of uniform speed vertical staggered shaft drive is derived, make the calculation formula of meshing limit line more simple. The meshing equation and the meshing limit line equation of ZN-type worm drive are derived. Through theoretical calculation, it is verified that the meshing limit line is the inherent characteristic of ZN-type worm pair and cannot be eliminated by modifying parameters. The meshing limit line is solved and some conclusions are drawn. The numerical results show that the meshing limit line exists on the worm tooth surface, which divides the contact area into two parts: effective area and ineffective area. The conjugate line of the meshing limit line is located in the middle of the worm gear tooth surface.